Question

Radius of a variable circle is changing at the rate of 5 cm/s. What is the radius of the circle at a time when its area is changing at the rate of 100 cm²/s? _____________​

Answer 1

Answer:

Let radius of the circle be r It is given that drdt = 5 cm/secNow area of circle is given by, A = π r2 dAdt = 2π r drdt , differentiate both sides

Answer 2

Answer: r= 10cm

Explanation: Let the radius of the circle be "r" and Area be "A"

Given: It is given that the radius of the variable circle is changing at the rate of $5cm/s$ and Also the area is changing at the rate of $100cm^{2} /s$

therefore, we can conclude that,

$dr/dt=5cm/s$, $dA/dt=100cm^{2}/s$........(1)

To find: $r=$$?$

Solution:

We know that ;

Area of the circle is given by (A) =π$r^{2}$

Differentiating both sides with respect to time, we get,

$dA/dt= 2rdr/dt$......(2)

Put the values from (1) in(2) we get,

$100=2*r*5$

On solving we get,

$r=10cm$